
where \({\mathbf {C}}\)  is a diagonal matrix. The model defined by Equation REF  is a fully-connected pairwise conditional random field. Exact maximum-a-posteriori inference on this CRF, needed both at training and testing phrase, is NP-hard [1]}. So they used max-product loopy belief propagation (LBP) to estimate the max-marginal probability
\(\hat{g}_i(e|D) \approx \max _{\begin{array}{c}e_1,...,e_{i-1}\\e_{i+1},...,e_n\end{array}} g(e_1,...,e_n|D)\) 
